CN104270713A - Passive type moving target track mapping method based on compressed sensing - Google Patents

Abstract

The invention discloses a passive type moving target track mapping method based on compressed sensing. The method comprises the steps that firstly, a wireless sensor network is deployed and configured; secondly, a target tracking model is established; thirdly, a moving object is tracked; fourthly, the target track vector is solved. The advantage of the compressed sensing in the aspect of sparse recovery is utilized, the track of the target is accurately mapped only through a small number of observation data, mapping is finished only through one-time calculation, and the problem that due to frequent positioning in an existing algorithm, calculating expenditure is high is avoided. The moving target track mapping method is very suitable for tracking the track of targets in large-scale scenes where wild animals live, and high-precision target track mapping can be achieved.

Description

Based on the passive type moving target track mapping method of compressed sensing

Technical field

The invention belongs to the applied technical field of wireless network, be specifically related to a kind of wireless sensor network passive type moving target track mapping method based on compressed sensing, the method is applied to the passive type target following of the wireless sensor network of wild animal.

Background technology

How effective wild animal has important ecologic niche and ecological functions at occurring in nature, is one of link indispensable in whole ecological chain, carry out monitoring and protect it, seems particularly important.Traditional conservation of wildlife adopts manual type hand-kept, statistics; therefore; there is a lot of drawback in traditional approach; as: lack chronicity, real-time; also certain difficulty and danger is had; in addition, space-time isolates, and is difficult to the comprehensive analysis data obtained being carried out to time, space, phenomenon.And the appearance of current wireless sensor network, provide technical support for solving the problem.

Wireless sensor network is made up of a large amount of distributed sensor nodes being deployed in area to be monitored, it combines the multiple fields technology such as sensor technology, wireless communication technology, embedded technology and computer technology, by various types of transducer, extensive, long-term, real-time acquisition is carried out to information such as the character of material, the state of environment and behavior patterns, and in the mode of self-organizing, perception data is sent to remote data center by 802.15.4 communication protocol.Wherein, the location technology of wireless sensor network be wild animal event trace monitoring provide effective solution.

The challenge of 4 aspects below the movement locus surveying and mapping technology existence of wild animal:

1) sparse deployment.The living environment and habit of not disturbing wild animal are monitored in a basic demand of wild animal monitoring.Therefore the least possible equipment is used to be one of demand towards the conservation of wildlife, i.e. sparse deployment.

2) equipment has nothing to do.Existing most localization method all requires object Portable device to be positioned (as GPS module, RFID label tag), but for wild animal Portable device is not easy to accomplish, and animal protection expert does not advise doing so yet.Therefore need when target not Portable device to realize location be one of demand towards the conservation of wildlife, namely equipment has nothing to do.

3) computing cost.Existing method, to the mapping of target passive type track, is all first locate the estimated position of different time point target have been linked up track mapping again, needs to position calculating at each time point, exist and frequently locate the problem causing computing cost large.Therefore need to reduce that frequently to locate to wild animal the problem causing computing cost large be one of demand towards the conservation of wildlife, i.e. computing cost.

4) track is openness.The position of wild animal movement locus process has openness compared with the position of monitored area.Therefore in order under the condition not reducing mapping precision, reducing mapping track desired data amount and reducing energy consumption is one of demand towards the conservation of wildlife, and namely track is openness.

Up to now, in wireless sensor network, there are many location technologies, have substantially been divided into following 4 classes:

The first kind: active location, i.e. object Portable device.As shown in Fig. 2 (a), sensor node evenly or random placement in locating area, signal that the equipment that object carries sends (as electromagnetic wave, infrared, ultrasonic wave etc.) can be detected by wireless sensor network, the signal sent at diverse location place equipment due to object is different, therefore the basic thought of these class methods is the changes being sent signal by checkout equipment, set up the respective function of signal intensity and position, and then object is positioned.If the people such as Kaltiokallio, Liu Yunhao are by the appearance of RSSI (Received Signal Strength Indicator) signal fluctuation detection target in wireless sensor network, and then position.The advantage of these class methods is positioning precision high (typically as GPS location), and because each object carries differentiable equipment, therefore Multi-target position is simple, is easy to add up destination number.But the shortcoming of the method needs target Portable device, the equipment do not met towards the conservation of wildlife has nothing to do demand.

Equations of The Second Kind: wait the passive type target localization based on study for representative with a top.As shown in Fig. 2 (b), sensor node is evenly deployed in monitored area, and adjacent node communicates, and object is movable in region can cause interference to the node of two communications.Carry out quantifications demarcation by the radio signal RSSI that is subject at diverse location place object interference, set up position and RSSI value disturb between relation.When disturbed node receives the RSSI value of one group of change, the position at object place can be released.The advantage of these class methods is that equipment has nothing to do, and does not need object Portable device also can to target localization.But it is intensive that the shortcoming of the method is node deployment, and cost is high, do not meet the sparse deployment requirements towards the conservation of wildlife.

3rd class: the RTI system proposed for representative with Joseph Wilson etc.As shown in Fig. 2 (c), sensor node is evenly deployed in locating area both sides, and all nodes are big vast model communication between any two.Object is movable in region can cause interference to the node of two communications.Similar with Equations of The Second Kind method, object is different to radio signal RSSI interference at diverse location place, sets up the relation between position and RSSI value.When the whole network node receives the RSSI value of one group of change, the position at object place can be released.The advantage of these class methods is the sparse deployment of network.Shortcoming needs any two node communications in the whole network, if the whole network nodes is 2M, then communication chain way is M (2M-1), and network energy consumption is high, for finite energy wireless sensor network and inapplicable.

4th class: wait the extendible passive type location for representative with a top.As shown in Fig. 2 (d), in locating area, become hexagon capable node deployment, a transmitting node is disposed at hexagonal center, and this node is with the node communication on each summit.Similar with Equations of The Second Kind method, object is different to radio signal RSSI interference at diverse location place, sets up the relation between position and RSSI value.When the whole network node receives one group of RSSI changing value, the position at object place can be released.Adopt the hexagon in mobile cellular network to dispose owing to disposing, therefore can dispose the seamless coverage of feasible region in larger locating area with multiple hexagon, each hexagon adopts same localization method, thus realizes the extensibility of location.The shortcoming of the method is accurate not to Multi-target position.As shown in Fig. 2 (d), when multiple target is not in same triangle time (as object 1 and object 2 or object 1 and object 3), this algorithm can provide the position of multiple target, but when multiple target is in same triangle time (as object 2 and object 3), multiple target Equivalent is become an object by this algorithm by mistake, and only provide the position of this equivalent object, become one and non-existent target by 2 target localizations, and the Multi-target position precision of the method depends on leg-of-mutton size.In order to sparse deployment, larger (2m to 3m) that triangle is generally chosen, therefore the Multi-target position error of the method is generally at 2m to 3m, and error is larger.

Secondly, in order to represent target location in Equations of The Second Kind, the 3rd class, four class methods, all adopt with the method for the grid of specific size by locating area gridding.Sizing grid directly affects positioning precision, and above-mentioned 3 class methods are for obtaining higher positioning accuracy, and grid generally chooses a smaller particular value.Above-mentioned 3 class methods are all the divisions under small-scale scene areas, and for large scale scene (as wild animal living environment), the division methods adopting this fixed value to attempt will certainly waste many energy and resources.

Summary of the invention

The defect existed for above-mentioned existing localization method or deficiency, the present invention proposes a kind of wireless sensor network passive type moving target track mapping method based on compressed sensing, surveys and draws the movement locus of wild animal.

In order to realize above-mentioned task, the present invention takes following technical solution:

Based on a passive type target trajectory mapping method for compressed sensing, comprise the following steps:

Step one, the deployment of wireless sensor network and configuration

To the monitored area disposed be needed to be divided into multiple grid, deployment transmitting node corresponding on two limits that monitored area is relative and receiving node, and a receiving node can only communicate by the transmitting node corresponding with it;

Step 2, sets up target following model

Time in monitored area without mobile object, multiple packets that the transmitting node that each receiving node receives its correspondence sends, and calculate the average signal strength values of these packets; Then a movable positioning object is set in monitored area, and makes this object each grid in monitored area successively, calculate object when being in each grid, the average signal strength values of multiple packets that each receiving node receives; According to the difference of the average signal strength values of twice calculating, build perception matrix A:

(formula 1)

In above formula, M is the number of transmitting node or receiving node, and N is the meshes number that monitored area is divided into, Δ R _a,b=R _a,b-F _a, R _a,bfor object be in b grid time, for the average signal strength values that a receiving node receives, F _afor in monitoring section without object time, the average signal strength values that a receiving node receives; A=1,2 ..., M, b=1,2 ..., N;

Step 3, the tracking of mobile object

Have mobile object in monitored area through out-of-date, K grid target trajectory vector theta of mobile object process represents:

Θ=[θ ₁..., θ _n] ^t(formula 2)

Note θ _j∈ Θ, j ∈ 1,2 ..., N}; When target is through a jth grid, θ _j=1, otherwise, θ _j=0;

Following expression is had according to compressive sensing theory:

Y=A Θ+n (formula 3)

In formula, n is white Gaussian noise;

Vectorial Y is handled as follows:

Z=Ω Y (formula 4)

Wherein, Ω=Φ A ^-1, Φ=orth (A ^t) ^t, orth (A) represents the orthogonalization of matrix A;

Formula 3 is substituted into formula 4 have:

Z=Ω (A Θ+n)=Φ A ^-1a Θ+n=Φ Θ+n (formula 5)

Vector constraint under, pass through l ₁norm solves, and expression formula is:

$\begin{array}{ccc}\min {\left|\right|\mathrm{\&Theta;}\left|\right|}_{l_1}& s.t.& {\left|\right|\mathrm{\&Phi;\&Theta;}-Z\left|\right|}_{l_2}<\mathrm{\&epsiv;}\end{array}$ (formula 6)

In formula 6, ε retrains the size of noisiness, and value is 3dBm; S.t. restriction relation is represented; l ₁for 1-norm, l ₂for 2-norm;

Step 4, solves target trajectory vector

Note Θ is track vector to be restored, represents true measurement and the difference estimating measured value with residual error r, and Q represents the pendulous frequency of artificial observation, set I _setrepresent the call number set of track vector Θ to be restored, I _set={ 1 .., N}; Variable c represents call number, and its value is from 1 to | I _set|, | I _set| be set I _setsize; Algorithm detailed process is as follows:

(1) initially make residual error r equal true measurement Y that a M receiving node receives the vectorial Y that RSSI average is formed ₀, i.e. r=Y ₀; Make call number c=1;

(2) I _setcall number be the element assignment of c to variable α, perform step (3);

(3) the call number c of track vector Θ to be restored is equaled the element θ of α _αvalue to Q, finds the value θ of the α of the 2-Norm minimum of the difference making residual values r and estimate measured value A Θ by 0 traversal _α, namely and record now θ _αvalue, then perform step (4);

Wherein, arg represents searching scope;

(4) after step (3) has traveled through Q time, Q { (ξ is defined ₁, θ ₁) ... (ξ _α, θ _α) ... (ξ _q, θ _q) combination, find ξ in Q combination _αminimum combination (ξ _α, θ _α), the element then the call number c of track vector Θ to be restored being equaled α replaces with θ _α, perform step (5);

(5) residual values r is updated to the minimum ξ found out in step (4) _α, perform step (6);

(6) call number set I is removed _setin, the minimum ξ found out in step (4) _αcorresponding index value is the call number that c equals α, then judges, as now met the condition of formula (7):

$\left\{\begin{array}{c}{\left|\right|r-A\&CenterDot;\mathrm{\&Theta;}\left|\right|}_{l_2}>\mathrm{\&epsiv;}\\ I_{\mathrm{set}}\&NotEqual;\mathrm{\&phi;},c\&le;\left|I_{\mathrm{set}}\right|\end{array}\right.$ (formula 7)

Then call number c added 1 and perform step (2), otherwise performing step (7);

(7) obtain track vector Θ to be restored, be the track vector Θ to be restored after upgrading in step (3), algorithm terminates.

The present invention compared with prior art has following advantage:

1. in the present invention, be provided with the tracking step of mobile object, by this step can by not in the same time target location hint obliquely at same monitoring area of space, thus disposablely survey and draw out target trajectory, avoid frequently locating the problem causing computing cost large, therefore only need a small amount of observation data, get final product accurate Drawing target trajectory;

2. be provided with target trajectory vector solution procedure in the present invention, propose Adaptive matching and follow the trail of (AMP) sparse recovery algorithms, accurately survey and draw out target trajectory when the unknown of target trajectory degree of rarefication (positional number of target process is unknown); The present invention compares with L1-magic algorithm with existing orthogonal matching pursuit algorithm OMP, provides higher reconstruction precision, and has used less observation data amount (reducing energy consumption);

3. mapping precision of the present invention is high, compares the track mapping precision that at least improve 63% with the existing RASS algorithm based on learning with the RTI algorithm based on tomography; Target trajectory for the large scale scene of wild animal existence is followed the tracks of very applicable, can realize the mapping of high-precision target trajectory, meet the demand of wild animal monitoring and protecting.

Accompanying drawing explanation

Fig. 1 is overall flow figure of the present invention;

Fig. 2 is 4 class existing target trajectory mapping algorithm schematic diagram;

Fig. 3 disposes schematic diagram based on the passive type target trajectory mapping of compressed sensing;

Fig. 4 truly tests scene graph;

Fig. 5 is when N=4 × 10 ⁴, during noise SNR=15dB, compare the track mapping error of AMP and 2 kind of sparse recovery algorithms.Fig. 5 (a) is at M=200, and the mapping error changed under different degree of rarefication compares; Fig. 5 (b) is at K=60, and the mapping error changed under different observation number of links compares;

Fig. 6 is the impact of target trajectory length K for mapping error;

Fig. 7 disposes number of links M to the impact of mapping error;

Fig. 8 is the effect diagram of stress and strain model size to mapping error;

Fig. 9 is mapping error Changing Pattern under large scale scene;

Figure 10 is that under real scene, target trajectory mapping is compared;

Figure 11 is that the inventive method compares with the energy ezpenditure of additive method;

Figure 12 is based on the passive type target trajectory mapping principle schematic diagram of compressed sensing;

Embodiment

Applicant is in the conservation of wildlife, in order to study the mechanics of wild animal in wild environment, need to obtain the motion track information that wild animal occurs in region in the wild, therefore, a kind of wireless sensor network passive type target trajectory mapping method based on compressed sensing is proposed, the basic ideas of the method are: (1) designs the sparse deployment scheme of a kind of network, reach the object reducing number of network node and reduce network energy consumption, (2) set up the target trajectory mapping model based on compressed sensing; The trace information modeling of target is represented, build perception matrix and compressed sensing expression formula, orthogonalization preliminary treatment is carried out to observation data and perception matrix, the trace information of target is obtained by compressed sensing decompression algorithm, (3) Adaptive matching follows the trail of (AMP) sparse recovery algorithms: Exact recovery sparse signal under degree of rarefication the unknown (positional number of target process is unknown), meets the demand of passive type target trajectory mapping; (4) arranging emulation experiment and truly testing regulates relevant parameter to evaluate the performance of CSTD method and AMP algorithm; Can cause different impacts to experimental result by studying relevant different parameters, we evaluate the present invention with true experiment at design and simulation experiment.

One, detailed step of the present invention

In order to finally realize the method for above-mentioned passive type target trajectory mapping, concrete operations are as follows, as shown in Figure 1:

Step one, the deployment of wireless sensor network and configuration

1. the division of monitored area:

The present invention disposes under real scene, take area as S=k ₁× k ₂covering monitored area, rectangular area, and be the grid of N number of ω × ω by this Region dividing; Namely with minimum rectangle by whole for monitored area covering.If monitored area length of side k ₁or k ₂the length of side ω of aliquant grid, then round up grid number, ensure locating area completely cover by grid, then by this N number of grid according to from left to right, order number consecutively from top to down: 1,2 ..., j ..., N-1, N.

2. the deployment of sensing node:

Be arranged in limit, one, monitored area (if Fig. 3 length of side is k ₁limit) on each grid outer ledge mid point on place a transmitting node, altogether dispose M transmitting node, the opposite side on this limit uses the same method deployment M receiving node.Arrange all wireless transceivers distance ground level and be H, the repetition test according to us draws, has good signal propagation characteristics as nodal distance ground height H=0.95m.In the scope of the circle being diameter with the line of all receiving nodes, dispose a base station, guarantee that the information of all receiving nodes can be sent to base station, and be connected with PC this base station, PC is used for collecting and analyzing data.Obviously this is a kind of scheme of sparse deployment facility, meets the demand of the sparse deployment of the conservation of wildlife.

3. network topology configuration:

As shown in Figure 3, M transmitting and M receiving node are numbered Tx successively respectively according to order from top to down _i, i=(1,2 ..., M) and Rx _p, p ∈ (1,2 ..., M).Network topology is set as, during and if only if i=p, and transmitting node Tx _iwith the receiving node Rx of its correspondence _pbetween can communicate.All nodes start communication simultaneously, Tx _ithe packet sent out only can Rx _preceive, each transmitting node sends a packet every 0.5s, and the data received (RSSI value) are transmitted to base station by corresponding receiving node, and the data received are transferred to PC by base station again.Under this network topology configuration, communication chain way is M, compared with the 3rd class methods introduced in background technology, when network node quantity is identical, communication chain way reduces to M bar by original M (2M-1), and therefore the energy consumption of wireless sensor network also reduces greatly.

After network topology sets, whether can proper communication between test node, for follow-up process is prepared.

Step 2, sets up target following model

Perception matrix A is set up before mapping

Under network working condition, entering of target can cause disturbance to the RSSI value received, and this method utilizes this disturbance to achieve passive type location.

(1) when there is no mobile object in locating area, each sending node sends 100 ~ 200 packets to the receiving node of oneself correspondence, 100 ~ 200 RSSI value that the sending node that receiving node receives oneself correspondence sends also ask its average, remember that the RSSI average that a receiving node receives is F _a, (a=1,2 ..., M);

(2) arrange a movable positioning object at locating area, the height of this positioning object is greater than H=0.95m; This object is allowed to travel through N number of grid of locating area successively, and make it stay for some time in each grid, ensure that each receiving node can receive 100 ~ 200 RSSI value in this grid, and when asking object to be arranged in each grid, the RSSI average that receiving node receives; Remember that the RSSI average that a receiving node receives is R _a,b, (b=1,2 ..., N); In this positioning object traversal monitored area after all grids, each receiving node obtains N number of RSSI average; Wherein, R _a,bwhen representing that Target Station occurs in b grid, the RSSI average that a receiving node receives;

(3) the disturbance Δ R because the RSSI value received for a receiving node when this single target occurs in b grid causes is calculated _a,bfor: Δ R _a,b=R _a,b-F _a;

(4) by the Δ R of M receiving node _a,b(a=1,2 ..., M; B=1,2 ..., N) construct the perception matrix A of M × N:

(formula 1)

Step 3, the tracking of mobile object

After utilizing positioning object to establish perception matrix A, the information of network design information and perception matrix A is preserved by PC, for the trajectory calculation of later mobile object submits necessary information.Then namely the sensor network of this deployment can be used as actual mobile object, as monitoring and the tracking of the animal track under wild environment.

Monitored area is the region that a slice is larger under real scene, after having mobile object to swarm into this region, because region has been divided into N number of grid, this mobile object is through monitored area, as it have passed through altogether K grid, from describing, when object is in certain grid above, can have an impact to the RSSI value that receiving node receives, then this K the grid track vector Θ that mobile object was accessed is expressed as follows:

Θ=[θ ₁..., θ _n] ^t(formula 2)

Note θ _j∈ Θ, j ∈ 1,2 ..., N}, i.e. θ _jfor any one element in the middle of Θ; When target is through a jth grid, θ _j=1, otherwise, θ _j=0.If no special instructions, when mentioning target at jth grid, refer in a jth net center of a lattice, when enough hour of grid and actual error within the acceptable range, still can reflect the situation of movement of target trajectory, now according to the deployment positional information of coordinate and the size of grid division, θ can be obtained by geometrical relationship _jrepresented unique two-dimensional coordinate (x _j, y _j).

Target of the present invention is tieed up measured value (i.e. the RSSI value of M bar link) by M exactly and is accurately obtained representing that the N of target trajectory ties up K-sparse vector Θ, and concrete steps are as follows:

(1) set Θ as track vector to be restored, namely target enters the track vector of random access grid after grid, has following expression according to compressive sensing theory:

Y=A Θ+n (formula 3)

Wherein, Y represents that there is target monitored area through out-of-date, the observation vector that the RSSI average that M receiving node receives is formed, Y=[y ₁, y ₂y _iy _m] ^t; A is the perception matrix set up in preceding step two; N is average to be 0 variance be 1 white Gaussian noise, Gauss refers to that probability distribution is normal function, and white noise refers to that its second moment is uncorrelated, and first moment is constant, refers to successively signal correlation in time, carrys out quantization means noise size with signal to noise ratio snr;

(2) orthogonalization process is carried out to perception matrix and observation vector:

When perception matrix column vector approximation is when orthogonal, track vector Θ to be restored can by Exact recovery.Therefore before recovery track vector Θ to be restored, first orthogonalization process is carried out to perception matrix and observation vector; Observation vector Y is handled as follows:

Z=Ω Y (formula 4)

Wherein, Ω=Φ A ^-1, Φ=orth (A ^t) ^t.Orth (A) represents the orthogonalization of matrix A, A ^-1and A ^trepresent the pseudo inverse matrix of A and the transposed matrix of A respectively, formula (3) is substituted into formula (4) to be had:

Z=Ω (A Θ+n)=Φ A ^-1a Θ+n=Φ Θ+n (formula 5)

(3) track vector Θ to be restored is obtained:

Because Φ is orthogonal matrix, therefore K-sparse vector Θ is tieed up for N, according to compressive sensing theory, when the dimension M of observation vector Z (or Y) meets M=O [Klog (N/K)] (O represents time complexity), track vector Θ to be restored can be constraint under, pass through l ₁norm solves, that is:

$\begin{array}{ccc}\min {\left|\right|\mathrm{\&Theta;}\left|\right|}_{l_1}& s.t.& {\left|\right|\mathrm{\&Phi;\&Theta;}-Z\left|\right|}_{l_2}<\mathrm{\&epsiv;}\end{array}$ (formula 6)

In formula (6), ε retrains the size of measurement noises, generally gets ε=3dBm; S.t. restriction relation is represented; l ₁and l ₂represent two kinds of different computings, l ₁for 1-norm, l ₂for 2-norm;

Can obtain the trace information of target according to the above-mentioned definition of track vector Θ to be restored, therefore, method of the present invention can solve by the disposable trace information to target, meets the demand that the conservation of wildlife is followed the tracks of target.

Step 4, solves target trajectory vector

For solving the track vector Θ to be restored of target, existing most of algorithm all requires the degree of rarefication knowing vector theta to be restored, namely need to know that target have passed through how many grids, but it is unpractical for obtaining K value in practical application in advance.For solving this problem, the present invention proposes Adaptive matching and follows the trail of (AMP) sparse recovery algorithms.

Just obtain track vector Θ to be restored after completing above-mentioned steps, then follow the trail of (AMP) sparse recovery algorithms by Adaptive matching and can solve Θ when degree of rarefication K (i.e. the grid number of target process) is unknown:

The core concept of 1.AMP:

(1) first find a maximum nonzero element is contributed to vector theta, this element is joined vector theta to be restored, and remains in successive iterations constant;

(2) based on the vector theta of previous step renewal, find the secondary large nonzero element of Θ contribution, this element is joined vector theta to be restored, and remains in successive iterations constant;

(3) repeat with this, until reach end condition.

2. specific algorithm realizes:

Represent true measurement and the difference estimating measured value with variable r, i.e. residual error, Q represents the pendulous frequency of artificial observation, as shown in figure 12, corresponding to the moment of the Q in Figure 12; Set I _setrepresent the call number set (call number is a kind of structure sorted to the element of vector, and as vector x=[4,5,2], then the call number of element 4 and element 5 is respectively 1 and 2) of track vector Θ to be restored, be set to I _set={ 1 .., N}.Variable c represents call number, and its value is from 1 to | I _set|, | I _set| be set I _setsize.

Algorithm detailed process is as follows:

(1) initially make residual error r equal true measurement Y that a M receiving node receives the vectorial Y that RSSI average is formed ₀, i.e. r=Y ₀; Make call number c=1;

(2) I _setcall number is element (the i.e. I of c _setc element) assignment to variable α, i.e. α=I _setc (), performs step (3);

(3) the call number c of track vector Θ to be restored is equaled the element θ of α _αvalue to Q, finds the value θ of the α of the 2-Norm minimum of the difference making residual values r and estimate measured value A Θ by 0 traversal _α, namely and record now θ _αvalue, then perform step (4);

Wherein, arg represents searching scope;

(4) after step (3) has traveled through Q time, Q { (ξ is defined ₁, θ ₁) ... (ξ _α, θ _α) ... (ξ _q, θ _q) combination, find ξ in Q combination _αminimum combination (ξ _α, θ _α), then upgrade the value of track vector Θ to be restored, update method is that the element call number c of track vector Θ to be restored being equaled α replaces with θ _α, perform step (5);

(5) upgrade residual values r, update method is the minimum ξ will found out in step (4) _αvalue is assigned to r, i.e. r=ξ _α, perform step (6);

(6) by the call number set I of track vector Θ to be restored _setcarry out cutting, remove the minimum ξ found out in step (4) _αcorresponding index value is the call number that c equals α, then judges, as now met the condition of formula (7):

$\left\{\begin{array}{c}{\left|\right|r-A\&CenterDot;\mathrm{\&Theta;}\left|\right|}_{l_2}>\mathrm{\&epsiv;}\\ I_{\mathrm{set}}\&NotEqual;\mathrm{\&phi;},c\&le;\left|I_{\mathrm{set}}\right|\end{array}\right.$ (formula 7)

Then call number c added 1 and perform step (2), otherwise performing step (7);

The implication of formula 7 is, with regard to above-mentioned acquisition residual values r with estimate that measured value A Θ (A is the perception matrix that step 2 is set up, and Θ is track vector to be restored) calculates: when residual values r and the 2-norm of the difference of estimation measured value A Θ be greater than threshold epsilon ( ), and, the call number set I of track vector Θ to be restored _setbe not empty (I _set≠ φ) time, after variable c is added 1, iterative computation again, otherwise just obtain track vector to be restored.

Inventor is found by great many of experiments, and when setting ε=3dBm, restoration errors is minimum, therefore generally gets ε=3dBm.

(7) obtain track vector Θ to be restored, be the track vector Θ to be restored after upgrading in step (3), algorithm terminates.

Below just complete Adaptive matching and follow the trail of (AMP) sparse recovery algorithms.

Obtain track vector to be restored through this algorithm process and be target trajectory vector theta:

Θ＝[θ ₁,…,θ _N] ^T

θ in target trajectory vector theta _jthe value of ∈ Θ is convertible into target through the real trace route left by grid, and namely target is through a grid θ _jgetting 1, otherwise get 0, by drawing real trace route, obtaining the path of the reality of target movement.

Due to the impact of noise etc. in reality, make target when jth grid, the element θ of Θ _jvalue is also non-zero or 1, also may deposit number between zero and one, therefore, work as θ _jwhen being greater than threshold value σ (generally σ=0.5) of threshold value one setting, by θ _jput 1, otherwise set to 0;

When target is repeatedly through a jth grid, θ _jvalue will be greater than 1, but now do not affect the mapping of track, so time still by above-mentioned threshold value diagnostic method by θ _jput 1.

Two, the inventive method henchnmrk test and the contrast experiment with other algorithms

1. evaluation index

The present invention's real trace weighs track mapping error with the mapping spacing of track and the ratio of sizing grid.

The real trace of hypothetical target is through K position (x ₁, y ₁), (x ₂, y ₂) ... (x _k, y _k), the mapping track of target by individual position become.Calculate all (x ₁, y ₁), (x ₂, y ₂) ... (x _k, y _k) and distance between any two, is then arranged in table by all distances according to nonincremental form, according to the true coordinate (x corresponding to this table middle distance calculated value _c, y _c) and estimation coordinate target trajectory mapping error TE can be calculated as follows:

$\mathrm{TE}==\frac{{\mathrm{\&Sigma;}}_{e=1}^{\min \{K,\hat{K}\}}\sqrt{{(x_e-{\hat{x}}_e)}^2+{(y_e-{\hat{y}}_e)}^2}}{\mathrm{\&omega;}\min \{K,\hat{K}\}},$ (formula 8)

Wherein, ω is that the Grid Edge of zoning is grown up little.

2. comparison other

For passive type target trajectory mapping method (CSTD method) superiority in track mapping based on compressed sensing that checking the present invention proposes, by it compared with existing two kinds of classic algorithm, namely based on the RASS algorithm of study and the RTI algorithm based on tomography.Note, (1) RASS algorithm mode of surveying and drawing target trajectory again of first locating traditionally is carried out; (2) RTI algorithm one panel region comes the position of estimating target but not an accurate coordinates, therefore using the estimated position of the center position coordinates of RTI estimation region as target.

Whether be better than existing algorithm for checking the sparse recovery algorithms of AMP in this paper and higher reconstruction precision can be provided, it is compared with L1-magic algorithm with famous orthogonal matching pursuit algorithm OMP.Note, OMP algorithm needs the degree of rarefication K knowing vector to be restored, and therefore we are by original end condition " iteration K time ", changes that " iteration is until residual error is less than threshold value (<10 into ^-6).

3. experiment initial condition is set

(1) emulation platform is built

Emulation is platform with Matlab, and required data are obtained by Free propagation model and diffraction model, and the relevant parameter value of this model is as shown in table 1.As shown in Figure 3, if wireless signal wavelength is λ, Tx _iand Rx _pbetween distance be d _i,ttx _ior Rx _pand the distance between target is d _i,t(or d _p,t).According to diffraction model, only just this link can be disturbed when target is positioned at the first Fresnel zone of link, therefore when target is positioned at jth grid, the RSSI measured value R of i-th link _i,jbe calculated as follows:

(formula 9)

Wherein, the radius size of first Fresnel zone, the path loss of i-th link, P _itx _itransmitting power, n is noise, carrys out quantization means noise size (w-o represents noiseless), D in emulation with signal to noise ratio snr _i,jbe because the appearance of target decays to the RSSI that link causes, be defined as follows

$D_{i,j}=20\log \left[\frac{\sqrt{2}}{2}\right|{\&Integral;}_v^{\&infin;}\exp \left(\frac{-\mathrm{img}}{2}\mathrm{\&pi;}{t}^2\right)\mathrm{dt}\left|\right]$ (formula 10)

In Fig. 3, h is effective depth, and its value is that object height deducts link apart from ground level, and img is imaginary part, D _i,jvalue and t irrelevant only relevant with range of integration ∞, v.

(2) each relevant parameter is determined

In emulation experiment, the performance by regulating following parameter to evaluate CSTD method: 1. K: the grid number of target process, the i.e. degree of rarefication of track vector Θ, 2. M: link number, the i.e. dimension of observation vector Y, 3. ω: the sizing grid of zoning.4. AS: the size in region.As nothing illustrates, the default value of these parameters is in table 2.

Table 1 simulation model relevant parameter and value

Table 2 emulation experiment parameter and acquiescence value

4. sparse recovery algorithms Performance comparision

For the sparse recovery superiority of AMP algorithm under degree of rarefication the unknown that checking the present invention proposes, it is compared with L1-magic algorithm with famous orthogonal matching pursuit algorithm OMP: Fig. 5 illustrates the track mapping error of AMP algorithm lower than OMP and L1-magic algorithm.As in Fig. 5 (a) at M=200, time K>20 (or 30), OMP (or L1-magic) algorithm starts to occur mapping error, i.e. evaluation index TE>0, and AMP algorithm is when K<70, all the time accurately can survey and draw target trajectory, namely keep TE=0 always.Fig. 5 (b) again demonstrates AMP algorithm and is better than OMP and L1-magic algorithm.As without making an uproar (w-o) under environment, as K=60, AMP algorithm at least needs 175 measured values accurately to survey and draw target trajectory, and L1-magic and OMP algorithm at least needs 185 and 200 measured values accurately to survey and draw target trajectory respectively.

In sum, the more above-mentioned two kinds of sparse recovery algorithms of classics of AMP algorithm can provide higher reconstruction precision, and have used less observation data amount (reducing energy consumption), therefore have certain superiority.

5. evaluate CSTD relevant parameter to the impact of mapping error

(1) the target trajectory length (i.e. the size of K) that can accurately survey and draw of CSTD method

Being interval by K with 10 is increased to 120 (namely constantly increasing the length of mapping track) by 10, and keeps other parameters as shown in table 2 constant.The maximum path length K that CSTD can accurately survey and draw as can be seen from Figure 6 is limited.As when K >=80, the mapping error TE of CSTD sharply increases.The reason that the performance of RTI algorithm is not so good as CSTD is, RTI needs more intensive deployment and more measured value (i.e. number of links), secondly, RTI only estimating target occur region but not particular location, even and if CSTD utilizes compressed sensing principle also can go out target trajectory by Exact recovery under a small amount of measured value, and CSTD provides the particular location of target.The mapping error of RASS algorithm is substantially constant, this is because RASS adopts and traditional first locates the method for surveying and drawing track again.The track mapped results of RASS is actually and carries out K the independent positioning result repeated to target, and therefore mapping error can not change because of K value.

(2) the track mapping error of CSTD and the relation of deployment number of links (i.e. M value)

Be that interval reduces to 35 (namely constantly removing the link of deployment) by 200 by M with 15, and keep other parameters as shown in table 2 constant.As seen from Figure 7, compared with disposing number of links with acquiescence, CSTD method accurately can survey and draw target trajectory under more sparse deployment, such as CSTD (w-o), when M reduces to by 200 the trend that error TE that track mapping error TE in the process of 175 is always 0, RTI and RASS algorithm then presents growth.The reason of this phenomenon is that the parameter value of CSTD still meets compressed sensing principle as M=175>log (N/K) ≈ 169, therefore accurately can survey and draw track when disposing more sparse than acquiescence.CSTD is better than the reason of RTI and RASS algorithm as described in first emulation.

(3) relation between CSTD track mapping error and stress and strain model size (i.e. ω value)

Be that interval is increased to 2.4m by 0.1m, then comparison object path length K=20,40,60, the track mapping error under 80 with 0.2m by sizing grid ω.Attention: when sizing grid ω changes, number of links M and grid number N also can change, according to being deployed with M=k herein ₁/ ω, N=k ₁k ₂/ ω ².Fig. 8 illustrates the mapping error under different sizing grid and K value, can find two rules: 1. under defining K value, when ω exceedes certain critical value, will there will be mapping error, and in non-linear growth; 2. K value is larger, occurs that the ω critical value of mapping error is less.The reason of these two rules is according to compressed sensing principle, ω demand fulfillment k feeling the pulse with the finger-tip mark path length; Namely the lower bound that accurately mapping target trajectory demand fulfillment is certain, and this boundary is about area size (k ₁and k ₂) and mapping track size (K) nonlinear function, demonstrate rule 1.; This boundary and K value are inversely proportional to, and demonstrate rule 2..

(4) mapping error of CSTD under large scale scene.

K is increased to 6600 by 60, by region area AS by 10 ⁴m ²be increased to 11 × 10 ⁴m ².Because area size has exceeded link communication scope, therefore with a series of subregion, it is covered.Simple period, if the size of every sub regions is still 100m × 100m.Simulation result Fig. 9 shows, the area size that CSTD accurately can survey and draw target trajectory depends on the maximum mesh number of target process.According to compressed sensing principle and first simulation result, the grid number that every sub regions accurately can survey and draw target process is 70, if therefore there is T sub regions, the so maximum target that can accurately survey and draw through grid number be 70T.If the grid number K<70T of target process, then CSTD accurately can carry out track mapping, as the part of TE=0 in Fig. 9.Otherwise mapping error TE obeys two rules below: 1. when AS fixes, K is larger, and TE is larger; 2. when K fixes, AS is larger, and TE is less.

6. the target trajectory mapping precision under real scene and the assessment of energy consumption thereof

(1) target trajectory accuracy evaluation

Experimentation:

Applicant is on the playground of school's spaciousness, and the open area choosing a S=8m*8m carries out the target trajectory mapping experiment of real scene as track mapping region.With the grid of length of side ω=0.5m by whole mapping Region dividing, the region of 8m*8m is divided into altogether the grid of N=64 0.5m*0.5m.And by this N number of grid according to order number consecutively from left to right, be from top to down be positioned at mapping limit, one, region on each grid outer ledge mid point on place a transmitting node, nodal distance ground 0.95m, amount to deployment 24 transmitting nodes.On the opposite side on this limit, use the same method deployment 24 receiving nodes, in distance receiving node 25m place's deployment base station, and is connected with a PC this base station.

Secondly, according to method setting network topology of the present invention, perception matrix A is set up.A height is that the people of 1.75m is as target to be surveyed and drawn by experiment scene as shown in Figure 4.After 24 receiving nodes collect RSSI value 30s, construct vectorial Y according to the method described above, on PC, finally obtained the motion track information of target by passive type target trajectory mapping method.

Experimental result:

Figure 10 illustrates the target trajectory mapped results under real scene, and CSTD has at utmost approached real trace, can obtain the minimum TE=0.17 of mapping error, and the mapping error TE of RTI and RASS is respectively 0.46 and 0.49 by (13) formula.While minimizing observation data amount, CSTD comparatively RTI and RASS at least improves the track mapping precision of (0.17-0.46)/0.46=63%.

(2) algorithm energy consumption assessment

Energy consumption assessment process:

For CSTD and RASS, RTI algorithm, constantly increase the observation number of links being deployed in monitored area, until mapped results meets given accuracy requirement, then calculate the energy ezpenditure of this algorithm.According to Jie's wireless communication model, the energy ezpenditure of every bar link can be calculated as E _radio=e ₁bb ²+ 2BE _e1c, wherein B is data package size bitwise, and b is linkage length (as shown in Figure 3), e ₁=100pJ/ (bit/m ²), E _e1c=50nJ/bit.In the present invention every sub regions deployment and arrange all identical, B=320bits, b=4m, each monitoring moment all sends 30 packets, only considers that the energy ezpenditure in some subregions compares during convenient at this.Be directed to given algorithm, when subregion is covered by M bar link, its energy consumption is E _radio=M × 0.96mJ.

Assessment result:

Figure 11 illustrates under different mean trajectory mapping errors, and the energy ezpenditure contrast of CSTD and RASS, RTI algorithm, can find out for reaching given accuracy requirement, the energy consumption that CSTD consumes is minimum.Its reason is that CSTD utilizes compressed sensing principle, go out the track of target, and RASS and RTI needs more observation data accurately to survey and draw the track of target by means of only a small amount of observation data with regard to energy Exact recovery.Figure 11 also shows the reduction along with track mapping error, and energy ezpenditure is in increase.Its reason is, when covering monitored area with more link, can reduce the error (as shown in Figure 7) of track mapping to a certain extent, therefore along with the reduction of track mapping error, energy consumption will increase.

Thus it is known, the present invention proposes a kind of passive type target trajectory mapping method based on compressed sensing, its advantage utilizes the advantage of compressed sensing in sparse recovery, the track of target is is only accurately surveyed and drawn out by a small amount of observation data, this method is by means of only once having calculated mapping simultaneously, avoids existing algorithm and frequently locates the problem causing computing cost large.The target trajectory of the large scale scene that movement locus mapping method of the present invention is survived for wild animal is followed the tracks of very applicable, can realize the mapping of high-precision target trajectory.

Claims (1)

1., based on a passive type target trajectory mapping method for compressed sensing, it is characterized in that, comprise the following steps:

Step one, the deployment of wireless sensor network and configuration

To the monitored area disposed be needed to be divided into multiple grid, deployment transmitting node corresponding on two limits that monitored area is relative and receiving node, and a receiving node can only communicate by the transmitting node corresponding with it;

Step 2, sets up target following model

Time in monitored area without mobile object, multiple packets that the transmitting node that each receiving node receives its correspondence sends, and calculate the average signal strength values of these packets; Then a movable positioning object is set in monitored area, and makes this object each grid in monitored area successively, calculate object when being in each grid, the average signal strength values of multiple packets that each receiving node receives; According to the difference of the average signal strength values of twice calculating, build perception matrix A:

(formula 1)

In above formula, M is the number of transmitting node or receiving node, and N is the meshes number that monitored area is divided into, Δ R _a,b=R _a,b-F _a, R _a,bfor object be in b grid time, for the average signal strength values that a receiving node receives, F _afor in monitoring section without object time, the average signal strength values that a receiving node receives; A=1,2 ..., M, b=1,2 ..., N;

Step 3, the tracking of mobile object

Have mobile object in monitored area through out-of-date, K grid target trajectory vector theta of mobile object process represents:

Θ=[θ ₁..., θ _n] ^t(formula 2)

Note θ _j∈ Θ, j ∈ 1,2 ..., N}; When target is through a jth grid, θ _j=1, otherwise, θ _j=0;

Following expression is had according to compressive sensing theory:

Y=A Θ+n (formula 3)

In formula, n is white Gaussian noise;

Vectorial Y is handled as follows:

Z=Ω Y (formula 4)

Wherein, Ω=Φ A ^-1, Φ=orth (A ^t) ^t, orth (A) represents the orthogonalization of matrix A;

Formula 3 is substituted into formula 4 have:

Z=Ω (A Θ+n)=Φ A ^-1a Θ+n=Φ Θ+n (formula 5)

Vector constraint under, pass through l ₁norm solves, and expression formula is:

$\begin{array}{ccc}\min {\left|\right|\mathrm{\&Theta;}\left|\right|}_{l_1}& s.t.& {\left|\right|\mathrm{\&Phi;\&Theta;}-Z\left|\right|}_{l_2}<\mathrm{\&epsiv;}\end{array}$ (formula 6)

In formula 6, ε retrains the size of noisiness, and value is 3dBm; S.t. restriction relation is represented; l ₁for 1-norm, l ₂for 2-norm;

Step 4, solves target trajectory vector

Note Θ is track vector to be restored, represents true measurement and the difference estimating measured value with residual error r, and Q represents the pendulous frequency of artificial observation, set I _setrepresent the call number set of track vector Θ to be restored, I _set={ 1 .., N}; Variable c represents call number, and its value is from 1 to | I _set|, | I _set| be set I _setsize; Algorithm detailed process is as follows:

(1) initially make residual error r equal true measurement Y that a M receiving node receives the vectorial Y that RSSI average is formed ₀, i.e. r=Y ₀; Make call number c=1;

(2) I _setcall number be the element assignment of c to variable α, perform step (3);

(3) the call number c of track vector Θ to be restored is equaled the element θ of α _αvalue to Q, finds the value θ of the α of the 2-Norm minimum of the difference making residual values r and estimate measured value A Θ by 0 traversal _α, namely and record now θ _αvalue, then perform step (4);

Wherein, arg represents searching scope;

(4) after step (3) has traveled through Q time, Q { (ξ is defined ₁, θ ₁) ... (ξ _α, θ _α) ... (ξ _q, θ _q) combination, find ξ in Q combination _αminimum combination (ξ _α, θ _α), the element then the call number c of track vector Θ to be restored being equaled α replaces with θ _α, perform step (5);

(5) residual values r is updated to the minimum ξ found out in step (4) _α, perform step (6);

(6) call number set I is removed _setin, the minimum ξ found out in step (4) _αcorresponding index value is the call number that c equals α, then judges, as now met the condition of formula (7):

$\left\{\begin{array}{c}{\left|\right|r-A\&CenterDot;\mathrm{\&Theta;}\left|\right|}_{l_2}>\mathrm{\&epsiv;}\\ I_{\mathrm{set}}\&NotEqual;\mathrm{\&phi;},c\&le;\left|I_{\mathrm{set}}\right|\end{array}\right.$ (formula 7)

Then call number c added 1 and perform step (2), otherwise performing step (7);

(7) obtain track vector Θ to be restored, be the track vector Θ to be restored after upgrading in step (3), algorithm terminates.